An economic enterprise, particularly a financial firm, insurance company, or government agency, often faces uncertainty in the future financial value of its assets and liabilities. These assets and liabilities can be brought to the enterprise via financial trading, or via financial or insurance underwriting, and then managed within a portfolio. In the prior art, the uncertainty of these assets and liabilities were evaluated differently, based on whether they were traded financial instruments, in a trading risk management environment, or, based on whether they were underwritten financial obligations, in an underwriting risk environment.
Pricing of Assets and Liabilities within a Trading Environment
When assets and liabilities are managed within a trading environment, such as where stocks, bonds, currencies, commodities, or other financial instruments are exchanged, uncertainty can be expressed as a probability distribution of potential future market prices. For each instrument, a probability distribution assigns a probability to each potential future price, as a potential outcome. Some outcomes increase, and others decrease, the future value of a portfolio that holds, and trades, these financial instruments.
For example, a mutual fund trader faces uncertainties in a stock portfolio because of volatilities in the underlying stock price. A municipal bond issuer from city government faces uncertainties in risk-free interest rates. A corporate treasurer faces uncertainties in strike prices for options issued to employees. A farmer faces uncertainties in soybean commodity futures prices before harvest time.
For each trading portfolio, a probability distribution of future prices can be assigned to each individual instrument, or, to any grouping of instruments, or, to the entire portfolio of instruments. The shape, skew, and other aspects of this probability distribution are fitted to historical records of past price movements for those instruments. This “fitted distribution” can then be used in quantitative models to anticipate future price movements.
Historical data for the price changes of stocks, bonds, currencies, commodities, and other financial instruments can be fitted to different kinds of probability distributions. These include parametric distributions generated by a simple mathematical function, such as normal, lognormal, gamma, Weibull, and Pareto distributions, and non-parametric distributions generated from a set of mathematical values, like those known from historical tables, or those generated from computer simulations.
In the prior art, computer-implemented systems and methods, and computer-readable media for use with computer means, for pricing financial instruments, were deficient because they could not accurately price, in a risk-neutral way, the vast majority of financial instruments whose price changes did not fit normal or lognormal probability distributions.
Pricing of Assets and Liabilities within an Underwriting Environment
Assets and liabilities can be managed within an underwriting environment, where, for example, credit, health care, pension, insurance, and other risks are assumed. Uncertainty can be expressed as a probability distribution of anticipated contract obligations. A probability distribution assigns a probability to each contract obligation, as an outcome. Some outcomes increase, and others decrease, the future value of a portfolio holding these obligations.
For example, a credit card issuer faces uncertainties because of customer delinquencies, defaults, renewals, prepayments, and fluctuations in outstanding balances. A utility company faces uncertainties in energy demand during extreme weather conditions. A hospital faces uncertainties in patient receivables. An insurance company faces uncertainties in premium receptions and claim payments. A reinsurer faces uncertainties of paying for hurricane and earthquake damages. A pension plan faces uncertainties of prolonged life expectancy.
For each underwritten portfolio, a probability distribution of anticipated obligations can be assigned to each individual contract, or to any collection of contracts, or to the entire portfolio of contracts. A parametric probability distribution can be fitted to historical records of past experience for those contract obligations. This “fitted distribution” can then be used in quantitative models to anticipate future contract obligations.
Historical data for contract obligations in credit, health care, pension, insurance, and other underwritten risks have been fitted to different kinds of probability distributions. These include parametric distributions generated by a simple mathematical function, such as normal, lognormal, gamma, Weibull, and Pareto distributions, and non-parametric distributions generated from a set of mathematical values, like those known from historical tables, or those generated from computer simulations.
In the prior art, computer-implemented systems and methods, and computer-readable media for use with computer means, were deficient because they could not accurately price, in a risk-neutral way, the vast majority of underwritten contract obligations whose cashflow outcomes did not fit normal or lognormal probability distributions. This was true even when portfolios were expressly underwritten for immediate transfer to another counterparty by true sale, trade, or even reinsurance.
Pricing of Underlying Risk Vehicles, Regardless of Whether they Consist of Assets or Liabilities, Traded or Underwritten
In the prior art, computer-implemented systems and methods, and computer-readable media for use with computer means, were deficient because they could not accurately price, in a risk-neutral way, the vast majority of financial instruments whose price changes did not fit normal or lognormal probability distributions.
Before this invention, computer-implemented systems and methods, and computer-readable media for use with computer means, were deficient because they could not accurately price, in a risk-neutral way, any managed portfolio of assets and liabilities whose entirety or parts were drifting from positive to negative value, or, from negative to positive value, over time.
With the explosion in computer applications, reams of historical data for financial instruments and contract obligations can now be gathered and processed instantly. Many computer simulation models can generate a sample distribution of possible outcomes for these traded and underwritten portfolios. For example, a derivative modeling firm can anticipate a price distribution for an underlying stock for a financial option. A catastrophe-modeling firm can anticipate a loss distribution for a geographic area after a simulated hurricane or earthquake.
Yet, with the increased availability of historically-known or computer-generated data, there is no accurate method for pricing the underlying risk, except in two special cases, applicable only to rare instances of probability distributions.
The first special case is the well-known Capital Asset Pricing Model, or CAPM, which relates the expected rate of return to the standard deviation of the rate of return. A standard assumption underlying the CAPM is that asset price movements have lognormal distributions, or, equivalently, that the rates of return for those asset price movements have normal distributions. The CAPM approach is deficient, however, when the historical asset returns do not have normal distributions.
The second special case is the Nobel Prize winning Black-Scholes formula for pricing options. Financial trading and insurance underwriting researchers have noted the similarity in the payoff function between a financial option and a stop-loss insurance cover. Again, a standard assumption underlying the Black-Scholes formula is that asset price movements have normal or lognormal distributions. Again, the Black-Scholes approach is deficient since the historical price movements of most capital assets do not have lognormal distributions.
To summarize, the historical data for traded and underwritten outcomes for assets and liabilities rarely resembles a normal or lognormal distribution. Most of the historical data fits other types of probability distributions. Most of the real-world traded and underwritten outcomes therefore cannot be effectively priced in a risk-neutral way by current valuation models, including those based on CAPM, Black-Scholes, or other implementations of modern options pricing theory.
There is a demand for a computer-implemented system and method, and a computer-readable medium for use with computer means, to effectively price all kinds of assets and liabilities, whether traded or underwritten, grouped or segregated, mixed or homogenized, in various and sundry ways, and whose probability distributions of uncertain outcomes, for any positive or negative values, at any level of detail, may be fitted, to any parametric type, including, but not limited to, normal, lognormal, gamma, Weibull, and Pareto distributions, as well as any nonparametric type, generated from any set of mathematical values, like from a computer.
In the United States in particular, the deregulation of banking, securities, and insurance, will encourage the integration of different portfolios of assets and liabilities, requiring such a unified approach.